Determination of the Fermi Energy of Diamond using Photoluminescence Spectral Analysis

Electronic band structures and the Fermi energy provide essential information for understanding the electronic properties of solids. In semiconductors, the Fermi energy level is determined by the donor and acceptor concentrations. For diamond, the relationship between the Fermi energy level and the donor-acceptor concentrations is highly nonlinear; therefore, experimental determination of the Fermi energy level is important. Here, we report a method to determine the Fermi energy of diamond based on photoluminescence (PL) measurement. The density-functional-theory (DFT) study by Deák et al. \cite{deak2014formation} showed the relationship between the Fermi energy and the formation energies of nitrogen-vacancy centers in the negatively charged (NV-) and neutrally charged (NV0) charge states. In the present method, we measure the relative populations of the NV- and NV0 centers from PL spectral analysis and, using these populations and the DFT result, determine the Fermi energy of the diamond samples. Moreover, we show the application of the method to study the spin coherence and the stability against the charge state conversion of the NV centers on several diamond samples. We also extend the method for the Fermi energy determination using the silicon-vacancy (SiV) center in diamond. The PL-based method is advantageous for determining the Fermi energy with high spatial and fast time resolutions, even in extreme environments, and can be extended to determine various wide band gap semiconductors.